Catgirls are more than fine. Just ears and optional tail do not furry make. Inhuman snouts and excessive body hair are the calling cards of furry. Or scales or gills or wings... Basically if the face and torso still look human, it doesn't make you furry. It just means you have the hots for a mildly genetically augmented being or a demon girl. Something that's no weirder than robot maids or human shaped aliens.
I object. You contradicted yourself there. You said having wings is furry, but then go on to cite demon girls, who generally have wings, as not furry. So, which is it?
Even if you like furry pictures you're not a furry. You're a furry when you start wanting to have sex in an animal suit or think of yourself as an animal instead of a human.